P-F-T
Please, please, search the board for posts on Gulfstream Academy and P-F-T. Read them through again.
The long and short of a place like Gulfstream is threefold. You do not want to get the reputation among your peers as one who cuts in line ahead of others. That's what happens when you P-F-T, which means pay for your training for a specific job with a specific company as a condition of hire. Do not confuse P-F-T with paying to learn how to fly and in doing so earning your Commercial certificate. Everyone must do that. Your peers work hard and long for years to afford flight training, get that first job, build time and climb the ladder. Cutting in front of them at low time via your (or Mom and Dad's or Auntie's) wallet will engender their resentment. In other words, very bluntly, you don't want to pi$$ off your coworkers.
Another reason not to choose Gulfstream is the impression it gives to H.R. people. They know that Gulfstream's former FOs paid for their jobs. Among other things, that will call your abilities into question. They, and others, will think the only reason you got the job is because you bought it. See my paragraph above for the problems that could cause.
The third reason is you can very well be turned loose from Gulfstream still as a very low-timer. Although you gained some 121/135 "experience" at Gulfstream, you still may not have enough time to meet normal commuter mins. That means you will have to build time to bridge the gap. That very well could mean you will have to spend more money to get your CFI certificate and instruct for a while. Nothing wrong with that at all, of course, but why should you be forced into that position to qualify for the next job after gaining all that wonderful "airline" experience at Gulfstream? You should have started from the beginning instructing and/or in a more typical low-time pilot job.
Finally, you have to take the malarkey dished out by all flight school "career counsellors" with a big grain of salt. These are not counsellors at all but sales people. Even the sales people at the most reputable schools sell a certain amount of pie in the sky. That's their job. Your job is to ferret out the facts.
Hope this helps. Good luck with your decision.